A Multiple Dependent State Sampling Plan for Percentile Based Life Tests under the Half Normal Distribution with Applications to Software and Device Reliability

Abstract

In modern reliability engineering, ensuring that product lifetimes meet specified percentile requirements is often more informative than relying on mean lifetime criteria, particularly for skewed or heavy‑tailed failure distributions. This paper develops a novel multiple dependent state (MDS) sampling plan for truncated life tests, assuming that product lifetimes follow a half‑normal distribution (HND). The proposed plan uses the percentile of the lifetime distribution as the quality benchmark, thereby providing enhanced protection against early failures. The operating characteristic (OC) function is derived, and an optimization framework is established to determine the minimum sample size together with the acceptance and rejection numbers such that the producer’s risk and consumer’s risk are simultaneously satisfied. Extensive tables of optimal plan parameters are presented for different truncation multipliers, percentile levels, and quality ratios. The results show that the MDS plan substantially reduces the required sample size compared to conventional single sampling plans. For example, at the sample size decreases from 48 (single plan) to 28 (MDS), a reduction of 41.67%. Two real‑world case studies, software failure times and electronic device lifetimes, demonstrate the practical applicability of the plan: a conforming software lot is accepted with minimal inspection, while a non‑conforming device lot is swiftly rejected. The proposed MDS plan offers an efficient, flexible, and statistically rigorous tool for reliability engineers who must balance inspection cost with stringent quality assurance.